We have studied charmless hadronic decays of B mesons into two-body final s
tates with kaons and pions and observe three new processes with the followi
ng branching fractions: B(B --> pi(+)pi(-)) = (4.3(-1.4)(+1.6) +/- 0.5) X 1
0(-6), B(B --> K(0)pi(0)) = (14.6(-5.1)(-3.3)(+5.9)(+2.1)) X 10(-6), and B(
B --> K(+/-)pi(0)) = (11.6(-2.7)(-1.3)(+3.0)(+1.4)) X 10(-6). We also updat
e our previous measurements for the decays B --> K(+/-)pi(+/-) and B+/- -->
K(0)pi(+/-).